Details

sample125.0ms

Algorithm

intervals

Results

80.0ms	174×	body	1280	valid
11.0ms	43×	body	640	valid
11.0ms	243×	body	80	valid
3.0ms	22×	body	320	valid
1.0ms	11×	body	160	valid

simplify2.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	14	8
2	26	8
3	40	8
4	56	8
5	62	8
6	71	8
7	88	8
8	248	8
9	788	8
10	3132	8
done	5000	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
5.2b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity` `add-log-exp`
4×	`add-sqr-sqrt` `frac-add`
3×	`flip3--` `flip--`
2×	`pow1` `add-exp-log` `neg-sub0` `exp-neg` `add-cube-cbrt` `sub-neg` `associate-+l+` `exp-diff` `diff-log` `sum-log` `add-cbrt-cube` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+l-` `flip3-+` `flip-+` `difference-of-squares`

Counts

2 → 35

Calls

2 calls:

10.0ms	(- (exp x) 2.0)
60.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series121.0ms

Counts

2 → 6

Calls

2 calls:

15.0ms	(- (exp x) 2.0)
106.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify656.0ms

Counts

41 → 41

Iterations

Useful iterations: done (655.0ms)

Iter	Nodes	Cost
0	93	511
1	215	465
2	832	445
done	5001	433

prune159.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
0.0b	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
0.0b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`add-exp-log` `associate-r`
12×	`*-un-lft-identity`
11×	`add-log-exp`
10×	`add-cube-cbrt`
8×	`unpow-prod-down` `add-cbrt-cube`
6×	`associate-l` `prod-exp` `unswap-sqr`
4×	`pow1` `sum-log` `sqr-pow`
2×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`associate-+r+` `distribute-lft-out`

Counts

4 → 75

Calls

4 calls:

19.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
27.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
20.0ms	(* 1/360 (pow x 6))
33.0ms	(* 1/12 (pow x 4))

series439.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
91.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
67.0ms	(* 1/360 (pow x 6))
52.0ms	(* 1/12 (pow x 4))

simplify1.1s

Counts

87 → 87

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	133	1068
1	343	934
2	1413	888
done	5001	879

prune383.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (+ (exp x) 2.0) (+ (* (- (exp x) 2.0) (exp x)) 1)) (* (exp x) (+ 2.0 (exp x))))
0.0b	(* (exp x) (+ 2.0 (exp x)))
0.0b	(* (- (exp x) 2.0) (exp x))
4.5b	(+ (* (- (exp x) 2.0) (exp x)) 1)

rewrite265.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-cbrt-cube`
16×	`add-exp-log`
14×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
9×	`flip3-+` `flip-+`
8×	`pow1` `add-cube-cbrt` `associate-l` `associate-/l/`
7×	`associate-r`
6×	`associate-*r/` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/`
2×	`pow-prod-down` `associate-/r/` `*-commutative` `unswap-sqr`
1×	`+-commutative` `distribute-rgt-in` `flip3--` `frac-2neg` `distribute-lft-in` `times-frac` `clear-num` `associate-/r` `sum-log` `flip--` `div-inv` `distribute-lft-out` `associate-/l` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 87

Calls

4 calls:

91.0ms	(/ (* (+ (exp x) 2.0) (+ (* (- (exp x) 2.0) (exp x)) 1)) (* (exp x) (+ 2.0 (exp x))))
48.0ms	(* (exp x) (+ 2.0 (exp x)))
64.0ms	(* (- (exp x) 2.0) (exp x))
57.0ms	(+ (* (- (exp x) 2.0) (exp x)) 1)

series326.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(/ (* (+ (exp x) 2.0) (+ (* (- (exp x) 2.0) (exp x)) 1)) (* (exp x) (+ 2.0 (exp x))))
39.0ms	(* (exp x) (+ 2.0 (exp x)))
43.0ms	(* (- (exp x) 2.0) (exp x))
89.0ms	(+ (* (- (exp x) 2.0) (exp x)) 1)

simplify4.2s

Counts

99 → 99

Iterations

Useful iterations: 2 (1.3s)

Iter	Nodes	Cost
0	174	1765
1	611	1686
2	4683	1409
done	5001	1409

prune461.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (+ (exp x) 2.0) (log (* E (exp (* (- (exp x) 2.0) (exp x)))))) (* (exp x) (+ 2.0 (exp x))))
0.0b	(* (exp x) (+ 2.0 (exp x)))
0.0b	(* (- (exp x) 2.0) (exp x))
3.0b	(log (* E (exp (* (- (exp x) 2.0) (exp x)))))

rewrite258.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-cbrt-cube`
18×	`add-exp-log`
14×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
11×	`pow1`
8×	`add-cube-cbrt` `associate-l` `prod-exp`
7×	`associate-r`
6×	`cbrt-unprod`
4×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `add-log-exp`
3×	`flip3-+` `rem-log-exp` `pow-prod-down` `flip-+`
2×	`associate-/r/` `log-pow` `*-commutative` `associate-/l/` `unswap-sqr`
1×	`distribute-rgt-in` `e-exp-1` `log-prod` `flip3--` `frac-2neg` `distribute-lft-in` `times-frac` `clear-num` `associate-/r` `flip--` `div-inv` `distribute-lft-out` `associate-/l` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 83

Calls

4 calls:

67.0ms	(/ (* (+ (exp x) 2.0) (log (* E (exp (* (- (exp x) 2.0) (exp x)))))) (* (exp x) (+ 2.0 (exp x))))
63.0ms	(* (exp x) (+ 2.0 (exp x)))
79.0ms	(* (- (exp x) 2.0) (exp x))
43.0ms	(log (* E (exp (* (- (exp x) 2.0) (exp x)))))

series960.0ms

Counts

4 → 12

Calls

4 calls:

671.0ms	(/ (* (+ (exp x) 2.0) (log (* E (exp (* (- (exp x) 2.0) (exp x)))))) (* (exp x) (+ 2.0 (exp x))))
33.0ms	(* (exp x) (+ 2.0 (exp x)))
57.0ms	(* (- (exp x) 2.0) (exp x))
200.0ms	(log (* E (exp (* (- (exp x) 2.0) (exp x)))))

simplify2.4s

Counts

95 → 95

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	156	1615
1	489	1484
2	3441	1186
done	5001	1184

prune496.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes44.0ms

Accuracy

0% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 0.6b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	15
1	17	15
done	17	15

end0.0ms

sample5.2s

Algorithm

intervals

Results

3.6s	5675×	body	1280	valid
581.0ms	7887×	body	80	valid
378.0ms	1257×	body	640	valid
105.0ms	607×	body	320	valid
35.0ms	308×	body	160	valid